Problem: What do the following two equations represent? $-x+4y = 5$ $-16x-4y = -5$
Answer: Putting the first equation in $y = mx + b$ form gives: $-x+4y = 5$ $4y = x+5$ $y = \dfrac{1}{4}x + \dfrac{5}{4}$ Putting the second equation in $y = mx + b$ form gives: $-16x-4y = -5$ $-4y = 16x-5$ $y = -4x + \dfrac{5}{4}$ The slopes are negative inverses of each other, so the lines are perpendicular.